Научная электронная библиотека ULRICH'S Periodicals Directory

Сибирский государственный университет
науки и технологий имени академика М.Ф. Решетнева

Сибирский аэрокосмический журнал
ISSN 2712-8970 (Print) ISSN 2782-5760 (on-line)

Сведения об образовательной организации

UDK 519.872
RESEARCH OF THE RETRIAL QUEUEING SYSTEM Μ(2) | B(x)(2) |1 WITH R-PERSISTENT EXCLUSION OF ALTERNATIVE CUSTOMERS
A. А. Nazarov, Y. E. Izmaylova
National Research Tomsk State University; 36, Lenin Av., Tomsk, 634050, Russian Federation
In this paper, we consider cosmic communication network operating under transmission protocols like CSMA (Carrier Sense Multiple Access). We have mathematical model of two companies competing for the right of possession of the network resource. Each company tries to promote its message on a broadcast communication channel, excluding messages of an alternative company. This model may be used for transmission of urgent messages by setting the priority of a particular company. A mathematical model of competing companies is the RQ-system with two arrival processes are described by the stationary Poisson process, the service time has the distribution function B1( x ) and B2 ( x ) , respectively, and exclusion of alternative customers. If at the time of arrival, customer of the first type finds the server busy with a customer of the first type, then it goes to the orbit 1 (in the orbit for customer of the first type). From the orbit 1, after the random delay, the customer is trying to occupy the server again. If at the time of arrival, customer of the first type finds the server busy with a customer of the second type, then an arrived customer with probability r1 replaces the customer, which was in service, and occupies the server, and with probability 1 – r1 it goes to the orbit 1. The same goes for the second type customer. We research retrial queueing system using the method of asymptotic analysis under condition of long delay in the orbits. For use this method we write system of differential Kolmogorov’s equations for the probability distribution of the number customers in the orbits and the server state, we have completed the transition to the system of differential equations for partial characteristic function. Using the method of asymptotic analysis we obtain the stationary probability distribution of server states and values of asymptotic means of the number of customers in the orbits. In particular, we analyze the weighted sum of gamma distribution and exponential distribution. It is found that for some values of function distribution parameters of service time and arrival process intensity, there is not any stationary regime. And there is such a stationary regime for some other values of distribution parameters of service time with any, no matter how great intensity values of λ1 and λ2 of arrival process. The results may be used for identify the number of messages that expect repeated requests and for the initial values of the parameters whereby the system operates optimally.
Keywords: retrial queueing system, alternative customer, r-persistent exclusion, asymptotic analysis, long delay.
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Nazarov Anatoly Andreevich – Dr. Sc., professor, Head of Department of Theory of Probability and Mathematical Statistics, National Research Tomsk State University. Е-mail: nazarov.tsu@gmail.com.

Izmaylova Yana Evgen’evna – postgraduate student, Department of Theory of Probability and Mathematical Statistics, National Research Tomsk State University. Е-mail: evgenevna.92@mail.ru.